A mathematical model of a river—shallow sea system used to investigate tide, surge and their interaction in the Thames—southern North Sea region

Abstract

A mathematical model is used to reproduce tidal and surge motion in the Thames Estuary and the Southern Bight of the North Sea. The model is based on a numerical finite-difference solution of the nonlinear hydrodynamical equations representing motion in the area. The equations are nonlinear in so far as they include quadratic bottom friction and allow for time variations in the total depth of water; the inclusion of advective terms is limited to the river. Solution of the one-dimensional equations for the river and the two-dimensional equations for the sea takes place within a single computational array. The scheme for calculating motion in the sea is similar to that developed by Heaps (1969), and the scheme for the river was developed by Rossiter & Lennon (1965). Tidal and surge motion within the model are reproduced by specifying the initial tidal contours of the sea, the external influences of surge and tidal oscillation along the open sea boundaries, and wind stresses over the sea surface. Computations have been concerned with generating lunar tidal oscillations for the construction of an M2 co-tidal chart, and investigating the interaction between tides and surges, in this region of shallow waters. The investigation of interaction involved calculating the sea’s response to the separate and combined effects of tidal and meteorological forces, whence the effects of a tide on a surge were deduced, possibly for the first time at offshore locations. Computed interaction phenomena for the period of a severe storm surge, 15 to 17 February 1962, were found to accord with the results of Proudman (19550, b, J957) and Rossiter (1961). Agreement between computed sea-level disturbances and actually recorded disturbances for this surge period revealed that the model has good potential for simulating sea level disturbances which occur in nature.